VECTORIAL SOLITARY WAVES IN OPTICAL MEDIA WITH A QUADRATIC NONLINEARITY

We search for self-trapped beams due to the vectorial interaction of t wo orthogonally polarized components of a fundamental harmonic and a s ingle component of the second harmonic in a quadratically nonlinear me dium. The basic set of equations for both the temporal and the spatial case is derived. The resulting two-parameter family of solitary waves is investigated by means of a variational approximation and by direct numerical methods. Several limiting cases and differences to the scal ar interaction in quadratic media are discussed. The propagation of st able solitary waves and mutual collisions are simulated and the decay of unstable solitary waves is demonstrated. We predict an internal bou ndary in the soliton parameter space which separates stable and unstab le domains.